Report

Background Noise • Definition: an unwanted sound or an unwanted perturbation to a wanted signal • Examples: – – – – – – Clicks from microphone synchronization Ambient noise level: background noise Roadway noise Machinery Additional speakers Background activities: TV, Radio, dog barks, etc. – Classifications • Stationary: doesn’t change with time (i.e. fan) • Non-stationary: changes with time (i.e. door closing, TV) Noise Spectrums Power measured relative to frequency f • White Noise: constant over range of f • Pink Noise: Decreases by 3db per octave; perceived equal across f but actually proportional to 1/f • Brown(ian): Decreases proportional to 1/f2 per octave • Red: Decreases with f (either pink or brown) • Blue: increases proportional to f • Violet: increases proportional to f2 • Gray: proportional to a psycho-acoustical curve • Orange: bands of 0 around musical notes • Green: noise of the world; pink, with a bump near 500 HZ • Black: 0 everywhere except 1/fβ where β>2 in spikes • Colored: Any noise that is not white Audio samples: http://en.wikipedia.org/wiki/Colors_of_noise Signal Processing Information Base: http://spib.rice.edu/spib.html Applications • ASR: – Prevent significant degradation in noisy environments – Goal: Minimize recognition degradation with noise present • Sound Editing and Archival: – Improve intelligibility of audio recordings – Goals: Eliminate noise that is perceptible; recover audio from old wax recordings • Mobile Telephony: – Transmission of audio in high noise environments – Goal: Reduce transmission requirements • Comparing audio signals – A variety of digital signal processing applications – Goal: Normalize audio signals for ease of comparison Signal to Noise Ratio (SNR) • Definition: Power ratio between a signal and noise that interferes. • Standard Equation in decibels: SNRdb = 10 log(A Signal/ANoise)2 N= 20 log(Asignal/Anoise) • For digitized speech SNRf = P(signal)/P(noise) = 10 log(∑n=0,N-1sf(n)2/nf(x)2) where sf is an array holding samples from frame, f; and nf is an array of noise samples. • Note: if sf(n) = nf(x), SNRf = 0 Stationary Noise Suppression • Requirements – low residual noise – low signal distortion – low complexity (efficient calculation) • Problems – Tradeoff between removing noise and distorting the signal – More noise removal normally increases the signal distortion • Popular approaches – Time domain: Moving average filter (distorts frequency domain) – Frequency domain: Spectral Subtraction – Time domain: Weiner filter (autoregressive) Auto regression • Definition: An autoregressive process is one where a value can be determined by a linear combination of previous values • Formula: Xt = c + ∑0,P-1ai Xt-i + nt • This is linear prediction; noise is the residue – Convolute the signal with the linear coefficient coefficients to create a new signal – Disadvantage: The fricative sounds, especially those that are unvoiced, are distorted by the process Spectral Subtraction • Noisy signal: yt = st + nt where st is the clean signal and nt is additive noise • Therefore: yt = xt – nt and estimated y’t = xt – n’t • Algorithm (Estimate Noise from segments without speech) Compute FFT to compute X(f) IF not speech THEN Adaptively adjust the previous noise spectrum estimate N(f) ELSE FOR EACH frequency bin: Y’(f)2 = (|Y(f)|a – |N(f)|a)1/a Perform an inverse FFT to produce a filtered signal • Note: (|Y(f)|a – |N’(f)|a)1/a is a generalization of (|Y(f)|2 – |N’(f)|2)½ S. F. Boll, “Suppression of acoustic noise in speech using spectral subtraction," IEEE Trans. Acoustics, Speech, Signal Processing, vol. ASSP-27, Apr. 1979. Spectral Subtraction Block Diagram Note: Gain refers to the factor to apply to the frequency bins Assumptions • Noise is relatively stationary – within each segment of speech – The estimate in non-speech segments is a valid predictor • The phase differences between the noise signal and the speech signal can be ignored • The noise is a linear signal • There is no correlation between the noise and speech signals • There is no correlation between noise in the current sample with noise in previous samples Implementation Issues 1. Question: How do we estimate the noise? Answer: Use the frequency distribution during times when no voice is present 2. Question: How do we know when voice is present? Answer: Use Voice Activity Detection algorithms (VAD) 3. Question: Even if we know the noise amplitudes, what about phase differences between the clean and noisy signals? Answer: Since human hearing largely ignores phase differences, assume the phase of the noisy signal. 4. Question: Is the noise independent of the signal? Answer: We assume that it is. 5. Question: Are noise distributions really stationary? Answer: We assume yes. Phase Distortions • Problem: We don’t know how much of the phase in an FFT is from noise and from speech • Assumption: The algorithm assumes the phase of both are the same (that of the noisy signal) • Result: When SNR approaches 0db the noise filtered audio has an hoarse sounding voice • Why: The phase assumption means that the expected noise magnitude is incorrectly calculated • Conclusion: There is a limit to spectral subtraction utility when SNR is close to zero Echoes • The signal is typically framed with a 50% overlap • Rectangular windows lead to significant echoes in the filtered noise reduced signal • Solution: Overlapping windows by 50% using Bartlet (triangles), Hanning, Hamming, or Blackman windows reduces this effect • Algorithm – Extract frame of a signal and apply window – Perform FFT, spectral subtraction, and inverse FFT – Add inverse FFT time domain to the reconstructed signal • Note: Hanning tends to work best for this application because with 50% overlap, Hanning windows do not alter the power of the original signal power on reconstruction Musical noise Definition: Random isolated tone bursts across the frequency. Why? Subtraction could cause some bins to have negative power Solution: Most implementations set frequency bin magnitudes to zero if noise reduction would cause them to become negative Green dashes: noisy signal, Solid line: noise estimate Black dots: projected clean signal Evaluation • Advantages: Easy to understand and implement • Disadvantages – The noise estimate is not exact • When too high, speech portions will be lost • When too low, some noise remains • When a noise frequency exceeds the noisy sound frequency, a negative frequency results – Incorrect assumptions: Negligible with large SNR values; significant impact with small SNR values. Ad hoc Enhancements • Eliminate negative frequencies: – S’(f) = Y(f)( max{1 – (|N’(f)|/Y(f))a )1/a, t} – Result: minimize the source of musical noise • Reduce the noise estimate – S’(f) = Y(f)( max{1 – b(|N’(f)|/Y(f))a )1/a, t} – Apply different constants for a, b, t in different frequency bands • Turn to psycho-acoustical methods: Don’t attempt to adjust masked frequencies • Maximum likeliood: S’(f) = Y(f)( max{½–½(|N’(f)|/Y(f))a )1/a,t} • Smooth spectral subtractions over adjacent time periods: GS(p) = λFGS(p-1)+(1-λF)G(p) • Exponentially average noise estimate over frames |W (m,p)|2 = λN|W(m,p-1)|2 + (1-λN)|X(m,p)2, m = 0,…,M- Acoustic Noise Suppression • Take advantage of the properties of human hearing related to masking • Preserve only the relevant portions of the speech signal • Don’t attempt to remove all noise, only that which is audible • Utilize: Mel or Bark Scales • Perhaps utilize overlapping filter banks in the time domain Acoustical Effects • Characteristic Frequency (CF): The frequency that causes maximum response at a point of the Basilar Membrane • Saturation: Neuron exhibit a maximum response for 20 ms and then decrease to a steady state, recovering a short time after the stimulus is removed • Masking effects: can be simultaneous or temporal – Simultaneous: one signal drowns out another – Temporal: One signal masks the ones that follow – Forward: still audible after masker removed (5ms–150ms) – Back: weak signal masked from a strong one following (5ms) Threshold of Hearing • The limit of the internal noise of the auditory system • Tq(f) = 3.64(f/1000)-0.8 – 6.5e-0.6(f/1000-3:3)^2 + 10-3(f/1000)4 (dB SPL) Masking Non Stationary Noise • Example: A door slamming, a clap – Characterized by sudden rapid changes in: Time Domain signal, Energy, or in the Frequency domain – Large amplitudes outside the normal frequency range – Short duration in time – Possible solutions: compare to energy, correlation, frequency of previous frames and delete frames considered to contain non-stationary noise • Example: cocktail party (background voices) – What would likely happen to happen in the frequency domain? How about in the time domain? How to minimize the impact? Any Ideas?